Lec_3 for bachelor of business class.pptx

business

1. STA 102 Statistics and Probability Descriptive Statistics: Frequency distribution and Graphical presentation

2. Frequency Distribution A frequency distribution is a grouping of data into mutually exclusive categories showing the number of observations in each class.

3. Constructing a frequency distribution involves: Determining the question to be addressed Collecting raw data Organizing data (frequency distribution) Presenting data (graph) Drawing conclusions

4. Definitions Class: In the process of condensation, raw data are assigned to some chosen groups of appropriate size. These groups are called classes . Frequency: The number of observations or values falling into each group or class is called class frequency or simply frequency .

5. Class Interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. The class interval should be equal. Class Limit: The smallest value of a class is known as lower class limit of the interval, while the largest value is known as the upper class limit of the interval. Class Mid-point: The midpoint of a class is a point that divides a class into two equal parts. This is the average of the upper and lower class limits.

6. Example: Dr. Tillman is the Dean of the School of Science, Socastee University. He wishes to prepare a report showing the number of hours per week students spend studying. He selects a random sample of 30 students and determines the number of hours each student studied last week. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6 Organize the data into a frequency distribution.

7. Step 1: Decide on the number of classes using the formula, 2 k > n Where, k = Number of classes n = Number of observations

8. There are 30 observations, so n = 30. 2 raised to the 5th power is 32. Therefore we should have at least 5 classes, i.e. k = 5.

9. Step 2: Determine the class interval or width using the formula Where, H = highest value, L = lowest value Round up for an interval of 5 hours. Set the lower limit of the first class at 7.5 hours, giving a total of 6 classes.

10. Step 3: Set the individual class limits. State clear class limits so you can put each observation into only one category. Step 4: Tally the observations into the classes. Step 5: Count the number of items in each class.

11. Frequency distribution of study hours

12. Class Midpoint: Find the midpoint of each interval using the following formula:

13. Relative Frequency Distribution: A relative frequency distribution shows the percentage of observations in each class.

14. Graphic Presentation of a Frequency Distribution The three commonly used graphic forms are: Histogram Frequency Polygon and Cumulative Frequency Distribution

15. Histogram A histogram is a graph in which the class midpoints are marked on the horizontal axis and the class frequencies on the vertical axis. Class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.

16. Histogram for hour spent studying

17. Frequency Polygon A frequency polygon consists of line segments connecting the points formed by the class midpoint and the class frequency .

18. Frequency Polygon for Hours Spent Studying

19. Cumulative Frequency Distribution A cumulative frequency distribution is used to determine how many or what proportion of data values are below or above a certain value. To create a cumulative frequency polygon, scale the upper limit of each class along the X-axis and the corresponding cumulative frequencies along the Y-axis.

20. Cumulative Frequency Table for Hours Spent Studying

21. Cumulative Frequency Distribution for Hours Spent Studying

22. Line Graph A line graph is particularly used to show the change or trend in a variable over time .

23. U.S. median age by gender of 10 years

24. Bar Chart A bar chart can be used to depict any of the levels of measurement (nominal, ordinal, interval or ratio). It is a form of presentation in which the frequencies are represented by rectangles separated along the horizontal axis and drawn as bars of convenience widths.

25. Construct a Bar Chart for the number of unemployed per 100,000 population for selected cities during 2001.

26. Bar Chart for the unemployment data

27. Pie Chart A Pie Chart, also known as Pie Diagram, is an effective way of presenting percentage parts when the whole quantity is taken as 100. The pie chart consists of a circle sub-divided into sectors, whose areas are proportional to the various parts into which the whole quantity is divided.

28. A sample of 200 runners were asked to indicate their favorite type of running shoe. Draw a pie chart based on the following information.

29. Pie Chart for Running Shoes